%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU692^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:29:02 AM UTC 2026
% Result : Theorem 3.69s 2.15s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 6 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 38 ( 12 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 130 ( 2 ~; 0 |; 0 &; 100 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 31 ( 0 ^; 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(func_decl,type,
func: $i > $i > $i > $o ).
thf(funcSet_decl,type,
funcSet: $i > $i > $i ).
thf(ap_decl,type,
ap: $i > $i > $i > $i > $i ).
thf(infuncsetfunc_decl,type,
infuncsetfunc: $o ).
thf(funcext_decl,type,
funcext: $o ).
thf(infuncsetfunc_def,definition,
( infuncsetfunc
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ C ) ) ) ) ).
thf(funcext_def,definition,
( funcext
= ( ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( func @ A @ B @ D )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ( ( ap @ A @ B @ C @ E )
= ( ap @ A @ B @ D @ E ) ) )
=> ( C = D ) ) ) ) ) ) ).
thf(1,conjecture,
( infuncsetfunc
=> ( funcext
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ! [D: $i] :
( ( in @ D @ ( funcSet @ A @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ( ( ap @ A @ B @ C @ E )
= ( ap @ A @ B @ D @ E ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext2) ).
thf(2,negated_conjecture,
~ ( infuncsetfunc
=> ( funcext
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ! [D: $i] :
( ( in @ D @ ( funcSet @ A @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ( ( ap @ A @ B @ C @ E )
= ( ap @ A @ B @ D @ E ) ) )
=> ( C = D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ C ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( func @ A @ B @ D )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ( ( ap @ A @ B @ C @ E )
= ( ap @ A @ B @ D @ E ) ) )
=> ( C = D ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( funcSet @ A @ B ) )
=> ! [D: $i] :
( ( in @ D @ ( funcSet @ A @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ( ( ap @ A @ B @ C @ E )
= ( ap @ A @ B @ D @ E ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU692^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:12:56 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (194ms).
% 1.21/0.97 % [INFO] Running in sequential loop mode.
% 1.82/1.38 % [INFO] eprover registered as external prover.
% 1.82/1.39 % [INFO] Scanning for conjecture ...
% 2.22/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.55 % [INFO] Type checking passed.
% 2.22/1.56 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.69/2.15 % External prover 'e' found a proof!
% 3.69/2.15 % [INFO] Killing All external provers ...
% 3.69/2.15 % Time passed: 1821ms (effective reasoning time: 1169ms)
% 3.69/2.15 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.69/2.15 % Axioms used in derivation (0):
% 3.69/2.15 % No. of inferences in proof: 4
% 3.69/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1821 ms resp. 1169 ms w/o parsing
% 3.69/2.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.69/2.20 % [INFO] Killing All external provers ...
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